SOLUTION: Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS

Algebra ->  Linear-equations -> SOLUTION: Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS       Log On


   

Question 32119: Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
For there to be an infinite number of solutions, the
equation (k+1)x+2(k+2)y=2k must be a multiple of
the equation 2x+5y=3
Let the multiplier by "a".
Then the equation is 2ax+5ay=3a
Then the following set of equation must be true:
k+1=2a
2k=3a
Then k=3a/2
Substitute that into k+1=2a to get:
(3a/2)+1=2a
(1/2)a=1
a=2
If a=2 then 2k=3(2) and k=3
Try It:
Substituting for "k" you get:
(3+1)x+2(3+2)y=2(3)
4x+10y=6
This is a multiple of the equation 2x+5y=3
Hope this helps.
Cheers,
Stan H.